The Collaborative International Dictionary of English v.0.48:

Execute \Ex"e*cute\, v. t. [imp. & p. p. Executed; p. pr. &
   vb. n. Executing.] [F. ex['e]cuter, L. executus, exsecutus,
   p. p. of exequi to follow to the end, pursue; ex out + sequi
   to follow. See Second, Sue to follow up, and cf.
   Exequy.]
   1. To follow out or through to the end; to carry out into
      complete effect; to complete; to finish; to effect; to
      perform.
      [1913 Webster]

            Why delays
            His hand to execute what his decree
            Fixed on this day?                    --Milton.
      [1913 Webster]

   2. To complete, as a legal instrument; to perform what is
      required to give validity to, as by signing and perhaps
      sealing and delivering; as, to execute a deed, lease,
      mortgage, will, etc.
      [1913 Webster]

   3. To give effect to; to do what is provided or required by;
      to perform the requirements or stipulations of; as, to
      execute a decree, judgment, writ, or process.
      [1913 Webster]

   4. To infect capital punishment on; to put to death in
      conformity to a legal sentence; as, to execute a traitor.
      [1913 Webster]

   5. To put to death illegally; to kill. [Obs.] --Shak.
      [1913 Webster]

   6. (Mus.) To perform, as a piece of music or other feat of
      skill, whether on an instrument or with the voice, or in
      any other manner requiring physical activity; as, to
      execute a difficult part brilliantly; to execute a coup;
      to execute a double play.

   Syn: To accomplish; effect; fulfill; achieve; consummate;
        finish; complete. See Accomplish.
        [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Execute \Ex"e*cute\, v. i.
   1. To do one's work; to act one's part or purpose. [R.]
      --Hayward.
      [1913 Webster]

   2. To perform musically.
      [1913 Webster]

WordNet (r) 3.0 (2006):

execute
    v 1: kill as a means of socially sanctioned punishment; "In some
         states, criminals are executed" [syn: execute, put to
         death]
    2: murder in a planned fashion; "The Mafioso who collaborated
       with the police was executed"
    3: put in effect; "carry out a task"; "execute the decision of
       the people"; "He actioned the operation" [syn: carry
       through, accomplish, execute, carry out, action,
       fulfill, fulfil]
    4: carry out the legalities of; "execute a will or a deed"
    5: carry out a process or program, as on a computer or a
       machine; "Run the dishwasher"; "run a new program on the
       Mac"; "the computer executed the instruction" [syn: run,
       execute]
    6: carry out or perform an action; "John did the painting, the
       weeding, and he cleaned out the gutters"; "the skater
       executed a triple pirouette"; "she did a little dance" [syn:
       perform, execute, do]
    7: sign in the presence of witnesses; "The President executed
       the treaty"

The Free On-line Dictionary of Computing (19 January 2023):

execution
execute
run

    The process of carrying out
   the instructions in a computer program by a computer.

   See also dry run.

   (1996-05-13)